Well, the country could just say no but once the country has said yes (probably after some very one-sided negotiation) the bank no longer has a choice. That is the case here: have American customers? Then you have to comply with the US rules.

The US is making a lot of trouble in banking. For example, if two non-US parties trade some US-based stock, then the whole thing has to be reported to the US specially independent from the normal reporting they have to do. I wish the US were a small enough player that everyone could just ignore this kind of nonsense but that's not the case at the moment.